arctan34

Arctan34 refers to the value of the inverse tangent function at the argument 34, i.e., the angle whose tangent is 34. In mathematical notation, arctan(34) is the unique number x in the interval negative to positive infinity that satisfies tan(x) = 34 with x in the principal value range of arctan, which is between −π/2 and π/2.

Numerical value. For positive arguments, arctan(34) lies in the first quadrant and is very close to π/2. A commonly used exact rearrangement is arctan(34) = π/2 − arctan(1/34). Using a short series expansion for arctan(1/34) or standard numerical evaluation gives arctan(34) ≈ 1.5413930277 radians, which is about 88.316 degrees. The relation arctan(34) = π/2 − arctan(1/34) often helps improve numerical stability when computing with small reciprocals.

Properties and context. The arctan function is the inverse of the tangent function on the interval (−π/2, π/2). Since 34 is positive, arctan(34) is a positive angle less than π/2. There is no simple closed-form expression for arctan(34) in terms of elementary constants; its value is typically obtained via numerical methods or high-precision calculators. In analysis or geometry, arctan(34) may arise when converting a large slope or rate into an angle, or when evaluating integrals and expressions that involve inverse trigonometric functions.

See also. arctan, inverse trigonometric functions, numerical evaluation of arctan.